Question

can someone help me with my hyperbolic functions topic

Answer 1

help please :)

Answer 2

I'm here. What's up?

Answer 3

thanks dude for the reply :)

Answer 4

No problem. So you have a question?

Answer 5

i really suck at calculus :(

Answer 6

is there a technique in hyperbolic functions ?

Answer 7

What do you mean by technique?
Do you have a specific question we can work on together?

Answer 8

for example what is tanh 0 ?

Answer 9

Ahh. Okay. All you need to do is remember what sinh, cosh, etc... really mean.

For tanh, it's:
\[\Large \tanh(x) = \frac{e^x - e^{-x}}{e^{x}+e^{-x}}\]
So replace x with zero.

Answer 10

ok,so my second problem is how to determine the e^0 ?

Answer 11

or e^-0 ?

Answer 12

Anything raised to zero is just 1.

Keep that in mind :)

Answer 13

Well, not really. zero raised to zero is... well, an anomaly, but e is not zero.

Answer 14

how about e^-0?will it be -1 ?

Answer 15

No... what is -0? :P
-0 is the same as zero :D

Answer 16

oh my,i really suck at math :D

Answer 17

i have another question :)
what is the derivative of tanh 4x?

Answer 18

Ohh... what's the derivative of tanh(x)?

Answer 19

And use the chain rule :)

Answer 20

how do you know that chain rule is the applicable process ?

Answer 21

If it's a composition... like a function within another function, then use the chain rule.
in this case, you have 4x inside tanh.

Answer 22

so what is the answer ?

Answer 23

First, tell me the derivative of tanh(x) :)

Answer 24

sech^2 ?

Answer 25

That's good. So the key to chain rule is to differentiate one at a time.
So we have
\[\Large \text{sech}^2(4x)...\]
We multiply this to the derivative of 4x... which is...?

Answer 26

4? right?

Answer 27

so the answer is sech^2 4?

Answer 28

Yup. So multiply 4 to this thingy, and you get your answer:
\[\Large 4\text{sech}^2(4x)\]

Answer 29

sech^2 4 made no sense, but I think I see what you mean.
How I wrote it is more elegant though :>

Answer 30

where did 4 come from ? before the sech2

Answer 31

The derivative of 4x.

Answer 32

and where did the 4x come from ?

Answer 33

inside tanh

This is how it works...
You differentiate something like tanh(4x)

So what you do, first, you differentiate the outermost function, in this case, tanh
So you get

sech²(4x)...
The next function inside is 4x, so you differentiate THAT, and then multiply:
Derivative of 4x is 4, so multiply it to sech²(4x)

And you get

4sech²(4x)

Answer 34

ohhhh i get it :)
how about \[\sinh^{2}x\]

Answer 35

Okay.... you have sinh here, BUT you also have a square. So this time, the outermost function is the square, right?

Answer 36

yes

Answer 37

So what's the derivative of square?
Derivative of x²?

Answer 38

2?

Answer 39

No... 2x :P

Answer 40

So you apply that to the sinh.
2sinh(x)...
But we're not done yet. After the 'square function' we have sinh.
What's the derivative of sinh(x) ?

Answer 41

cosh x

Answer 42

Right. So you multiply that to 2sinh(x)
and you're done :)

2sinh(x)cosh(x)

Answer 43

so if is see a square i should multiply it to the equation ?

Answer 44

No... see, with sinh^2 (x)
The key to chain rule is to treat the outermost function as the ONLY function for a while, and the rest as just one big fancy x.

sinh^2 (x), treat sin(x) as just one big fancy x, and differentiate.

2sinh(x)

Now differentiate sinh(x) itself.

2sinh(x)cosh(x)

Answer 45

ahhh ok :)
what about sinhxtanhx?

Answer 46

should i use product rule ?

Answer 47

Yes :)

Answer 48

so it will be derivative of sinhx*tanhx+sinhx*derivative of tanhx ?

Answer 49

Yup :)

Answer 50

so it will be coshc*tanhx+sinhx*sech^2 x?

Answer 51

Very good :)

Answer 52

cosh(x) by the way, not coshc

Answer 53

so that will be the answer ?
ahhh right sorry my bad :)

Answer 54

Yes, that's the answer :)

Answer 55

hahaha i improved .1 % in calculus :)

Answer 56

Although...cosh(x)tanh(x)... this can be simplified :)

Answer 57

so what is the final answer ?

Answer 58

That's for you to find out :)

Answer 59

cosh(x)tanh(x) simplify it...
remember, tanh(x) = sinh(x)/cosh(x)

Answer 60

so it will be sinhx ?

Answer 61

Very good :)

Answer 62

i have another sample :)
xcoshx
so will it be another product rule ?

Answer 63

Yup :)

Answer 64

so it will be derivative of x*coshx+x*derivative of cosh x?
1*coshx+x*sinhx ?

Answer 65

Yes :)

Answer 66

that's the answer already ?

Answer 67

Very good :)

Answer 68

hahaha can you help me in all of my assignment? :)

Answer 69

as long as I'm awake. where are you from anyway?

Answer 70

philippines,you ?

Answer 71

Well, as long as you can stay awake, then :)

Answer 72

so the 5th question in my assignment
sinh(x^2)

Answer 73

Okay. Outermost function is sinh.
What is the derivative of sinh ?

Answer 74

cosh x

Answer 75

Good.
cosh(x^2)
Next function is x^2. What is the derivative of x^2 ?

Answer 76

2x

Answer 77

so it is cosh 2x?

Answer 78

You then multiply this to cosh(x^2)
You get
2x cosh(x^2)
And this is your answer :)

Answer 79

how will i know if i had a n outermost function?

Answer 80

The one that seems to 'contain' all the other functions.

Or you can say the function that is not acted upon by another function.

Here, there is nothing acting on cosh, so that's the outermost.

Answer 81

huh?i dont get it

Answer 82

... tagalog? haha

Answer 83

opo hahaha

Answer 84

wag mo akong gamitan ng 'opo' XD
baka nga mas bata pa ako sayo eh :P

Anyway

lahat nung mga function sa sinh(x^2) nasa loob ng sinh.

Answer 85

ndi pa rin gets :D

Answer 86

hirap ipaliwanag eh... uhh

Answer 87

x^2 nasa loob ng sinh?
Wala akong ibang maisip na paraang sabihin :D

Answer 88

hahaha ok na un next question :)\[\frac{ 1-coshx }{ 1+coshx }\]

Answer 89

ndi naman sa minamaliit kita pero 100%sure ka ba sa mga sinasagot mo ? wag mo sanang masamaiin

Answer 90

sure.

Answer 91

Use quotient rule.

Answer 92

hahaha pano ung sagot ?

Answer 93

Quotient rule nga eh.

Answer 94

so (1+coshx)*derivative(1-coshx)-derivative(1+coshx)*(1-coshx)/(1+cosh)^2